Question

A first aid kit in the shape of a regtangular prism has a volume of 18,689cm³. The width of the kit is equal to the quarter of its length. The width of the kit is also equal to half its height. Determine the length, width, and height of the first aid kit. round to the nearest tenth.

Answer 1

The length, width, and height of the first aid kit are approximately 31.6 cm, 7.9 cm, and 3.95 cm respectively.

Step-by-step explanation:

Let the length of the first aid kit be 'l' cm. According to the given information, the width is equal to one-fourth of its length, so the width is 'l/4' cm. The height is equal to half the width, so the height is '(l/4)/2' cm.

Given that the volume of the first aid kit is 18,689 cm³, we can use the formula for the volume of a rectangular prism to find the value of 'l'. The formula is:

V = l * w * h

Substituting the values, we have:

18,689 = l * (l/4) * ((l/4)/2)

Simplifying the equation, we get:

18,689 = (l³/32)

To solve for 'l', we can take the cube root of both sides:

l = (32 * 18689)^(1/3)

Calculating the value, we have:

l ≈ 31.6 cm

So, the length of the first aid kit is approximately 31.6 cm. The width would be 'l/4' and the height would be '(l/4)/2'.